Find the volume generated by revolving the area enclosed by the curve x² + y = 25 about the y-axis.

Q: - Find the volume of the solid generated by revolving the region Enclosed by the curve (y-√√4x²,…

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Q: If the area of the curve y = sinx from x = 0 to x = π is revolved about the y=axis i, what is the…

A: The given curve is: y=sin x      from  x=0  to  x=π

Q: Find the volume of the solid generated by the area bounded by the curve y = x³,x = 1,x = 2 and y = x…

A: The volume of a region is the integration of the area of the region. It can be calculated using…

Q: Find the volume formed by revolving about the line y = 2a, the area bounded by that line, the curve…

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Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

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Q: Find the volume generated by the area bounded by the parabola x = Vay , and the line y = b that is…

A: As per our guidelines, we are suppose to answer only one question. kindly repost the question as the…

Q: The volume generated when ℝ is rotated about the x-axis.

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Q: Find the volume generated by revolving the area bounded by y = 1 - x³, OX and OY about the x-axis.

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Q: Find the volume produced by rotating the bounded region around the line y = 3 in the first quadrant…

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Q: Find the volume generated by revolving the area bounded by y=ex, x=0 and y=0 about the y-axis.

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Q: Find the volume of the solid generated by revolving the “triangular” region bounded by the x-axis,…

A: Given information:

Q: ) Find the volume formed by rotating the region enclosed by: x = 3y and y = x with y > 0 about the…

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Q: Find the volume generated by revolving the region above the curve y=x3 , under the line y=1, and…

A: Given: y=x3, y=1, x=0 & x=1 From the given curve the bounded region is as shown below: Apply…

Q: Find the volume swept out by revolving the region bounded by the y-axis and the graph of x = t (1 -…

A: Given,

Q: The area bounded by the parabolas y² = 4x and x² = 4y is revolved about the y-axis. Find the moment…

A: The given equation of the parabolas are, y2=4x and x2=4y.

Q: Find the volume generated if the area bounded by the curve x2 = y - 2 is revolved about the x –…

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Q: Find the volume generated if the area bounded by the curve x² = y – 2 is revolved about the x-axis.

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Q: Find the volume generated by revolving the area enclosed by the curve x^2+y^2=16 about the y-axis.

A: here volume is ∫πy2dx here the limit is if we put y=0 in equation so x range from -4 to 4 so   V=…

Q: Find the volume generated by revolving the area under the curve y=e^x from x=0 to x=1 about the…

A: Volume of the solid obtained by revolving x=g(y) about x-axis is given by,                   V =…

Q: Find the volume generated by revolving the curve y = cos(2x) about the x-axis, 0 < < 4

A: Given:       y=cos(2x) , 0≤x≤π4

Q: Find the volume if an arch of y=sin⁡2x (bounded by the x-axis) is revolved about the x-axis

A: Volume of revolving  of y = f(x) about X-axis  Vol =∫abπ(f(x))2dx

Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

A: When x=5 then  x=y255=y25y2=25y=5 So y is from 0 to 5 in the figure.

Q: Find the volume obtained by rotating the curve y = sin² x around the r-axis.

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Q: Find the volume generated by revolving the area enclosed by the curve x2 + y? = 9 about the x-axis.

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Q: Find the volume generated by revolving one arch of the curve y = sin x about the x-axis.

A: Let the bounds of one arch of the sine curve be 0 and pi. Then, the volume generated by revolving…

Q: Find the volume generated by revolving the area bounded by y² - 4y - 4x + 4 = 0 and x = 1 about the…

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Q: FIND THE VOLUME GENERATED BY REVOLVING THE AREA POUNDED BY THE L'INES Xt y=6,x=0 AID y=0, about…

A: The Washer Method: The volume generated by revolving the area bounded by the curves y=f(x) and…

Q: 3. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

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Q: Find the volume of a solid obtained by revolving the curve x2=y-3 about x-axis from x=1 to x=3

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Q: Find the volume of the solid generated by rotating the area bounded by the y=sqrt(x-1) and y=(x-1)^2…

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Q: Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 25 about the line y…

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Q: Find the volume generated if the area bounded by the curve x? = y – 2 is revolved about the x- axis.

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Q: Determine the volume generated by revolving the region in the first quadrant bounded by the curves…

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Q: Find the volume, if an area bounded by an asteroid I = cos t y = sin³ t ve y = -/I+x ,y-axis, and…

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Q: Find the volume of the solid generated by revolving the shaded region about the given axis.

A: We need to find volume.

Q: Find the volume swept out by revolving the region bounded by the x-axis and the graph of x = 2t, y =…

A: Given that x = 2t and y = t(2–t). Obtain the interval of integration as follows.

Q: Find the volume generated by revolving the area bounded by   xy=4, x=1, x=4 and the x-axis about the…

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Q: Find the volume of the solid obtained by revolving the area enclosed by y = 2x, y = 2 and r = 0…

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Q: Find the volume generated by revolving the area enclosed by the curve 4y² = 4x²-x+ about the y-axis.

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Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y = -2 about the…

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Q: find the volume of the solid formed by revolving the area bounded by y = sin(x^2), x epsilon…

A: Given that y=sinx2 , 0,π find the volume of the solid obtained by rotating around y axis…

Q: Find the volume generated by revolving the area bounded by the parabolic arc Vx + Jy = Va and the…

A: Given problem:- Find the volume generated by revolving the area bounded by the parabolic arc √x + √y…

Q: Find the volume generated by revolving the area enclosed by the curve x2 + y? = 25 about the y-axis.

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Q: Find the volume generated by revolving the area enclosed by the curve x-+y3D25 about the line…

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Q: Find the volume generated by revolving the area enclosed by the curve 4y² = 4x²-x* about the y-axis.

A: Hint: First obtain the values of x for which y is zero to obtain the limits of the integration. Now,…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.